{"paper":{"title":"Extremal hypergraphs for matching number and domination number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Liying Kang, Shan Li, Yanxia Dong","submitted_at":"2016-11-21T01:42:55Z","abstract_excerpt":"A matching in a hypergraph $\\mathcal{H}$ is a set of pairwise disjoint hyperedges. The matching number $\\nu(\\mathcal{H})$ of $\\mathcal{H}$ is the size of a maximum matching in $\\mathcal{H}$. A subset $D$ of vertices of $\\mathcal{H}$ is a dominating set of $\\mathcal{H}$ if for every $v\\in V\\setminus D$ there exists $u\\in D$ such that $u$ and $v$ lie in an hyperedge of $\\mathcal{H}$. The cardinality of a minimum dominating set of $\\mathcal{H}$ is the domination number of $\\mathcal{H}$, denoted by $\\gamma(\\mathcal{H})$. It was proved that $\\gamma(\\mathcal{H})\\leq (r-1)\\nu(\\mathcal{H})$ for $r$-un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06629","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}